| eBook ISBN: | 978-1-4704-0198-6 |
| Product Code: | MEMO/129/613.E |
| List Price: | $45.00 |
| MAA Member Price: | $40.50 |
| AMS Member Price: | $27.00 |
| eBook ISBN: | 978-1-4704-0198-6 |
| Product Code: | MEMO/129/613.E |
| List Price: | $45.00 |
| MAA Member Price: | $40.50 |
| AMS Member Price: | $27.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 129; 1997; 77 ppMSC: Primary 20
This memoir contains a complete classification of the finite irreducible 2-subgroups of \(GL(4, {\mathbb C})\). Specifically, the author provides a parametrized list of representatives for the conjugacy classes of such groups, where each representative is defined by a generating set of monomial matrices. The problem is treated by a variety of techniques, including elementary character theory, a method for describing Hasse diagrams of submodule lattices, and calculation of 2-cohomology by means of the Lyndon-Hochschild-Serre spectral sequence. Related questions concerning isomorphism between the listed groups, and Schur indices of their defining characters, are also considered.
Features:
- A complete classification of a class of \(p\)-groups
- A first step towards extending presently available databases for use in proposed “soluble quotient algorithms”
- Groups presented explicitly; may be used to test conjectures or to serve generally as a resource in group-theoretic computations
ReadershipGraduate students and research mathematicians interested in group theory and representation theory.
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Table of Contents
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Chapters
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Introduction
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1. Preliminaries
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2. The isomorphism question
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3. The case $T = V_4$
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4. The case $T = C$
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5. The case $T = D$
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6. Full solutions
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7. Schur indices
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This memoir contains a complete classification of the finite irreducible 2-subgroups of \(GL(4, {\mathbb C})\). Specifically, the author provides a parametrized list of representatives for the conjugacy classes of such groups, where each representative is defined by a generating set of monomial matrices. The problem is treated by a variety of techniques, including elementary character theory, a method for describing Hasse diagrams of submodule lattices, and calculation of 2-cohomology by means of the Lyndon-Hochschild-Serre spectral sequence. Related questions concerning isomorphism between the listed groups, and Schur indices of their defining characters, are also considered.
Features:
- A complete classification of a class of \(p\)-groups
- A first step towards extending presently available databases for use in proposed “soluble quotient algorithms”
- Groups presented explicitly; may be used to test conjectures or to serve generally as a resource in group-theoretic computations
Graduate students and research mathematicians interested in group theory and representation theory.
-
Chapters
-
Introduction
-
1. Preliminaries
-
2. The isomorphism question
-
3. The case $T = V_4$
-
4. The case $T = C$
-
5. The case $T = D$
-
6. Full solutions
-
7. Schur indices
